Quality of image improves with the number of gray shades pulse width modulation [1] and frame modulation [2] add gray shade capability to liquid crystal displays. The number of gray shades that can be displayed with these techniques is limited because the number of time intervals in a cycle increases linearly with the number of gray shades. In a matrix display with N address lines, N.(G−1) time intervals are necessary to display G gray shades. Flicker will be observed in the display if a large number of gray shades are displayed using frame modulation. The smallest time interval in pulse width modulation may be comparable or even less than the RC time constant (product of output resistance of drivers and equivalent capacitance of pixels) when the number of gray shades is large. Error in the RMS voltage across pixels due to distortion in the addressing waveforms will result in poor brightness uniformity among pixels that are driven to the same state in pulse width modulation when the number of gray shades is large. Another important consideration is the error in the RMS voltage across pixels as described next. The difference of RMS voltages across ON and OFF pixels is small in passive matrix displays. For example, the ON pixels get a voltage that is about 10% higher than that of OFF pixels in a matrix display with 100 address lines. The difference in RMS voltage across pixels that are driven to any two adjacent gray shades is even smaller and it decreases with increase in number of gray shades. The difference in RMS voltages of neighboring gray shades is about 0.625% for 16 gray shades, 0.156% for 64 gray shades and about 0.039% for 256 gray shades in a display where in 100 address lines are multiplexed. It is obvious that the error in the RMS voltage across the pixels has to be small as the number of grayscales is increased to ensure good brightness uniformity among pixels that are driven to the same gray shade. Error in the RMS voltages is primarily due to the following reasons:                a) Addressing waveforms consist of select or data voltages and any error in these voltages will contribute to the error in the RMS voltage across pixels.        b) Addressing waveforms have many abrupt (step like) transitions and the distortion in these steps due to RC time constant of the driver circuit will also contribute to error in RMS voltage across pixels.        
While the error in voltages of the addressing waveforms can be almost eliminated with a well-designed voltage level generator (VLG), the distortions in the addressing waveforms cannot be eliminated but can be minimized as described in the following text.                a) Reduce the RC time constant of the drive circuit by reducing R and/or        b) Increase the duration of the select time so that it is much larger than the RC time constant.        
Output resistance of the driver circuit can be decreased either by buffering each output of the driver integrated circuit or by reducing the ON resistance of the analog switches in the multiplexers that select the voltages of the addressing waveforms. Both will increase the die size of the driver integrated circuit. It is expensive to decrease the output resistance or the ON resistance because of the large number of stages in the driver integrated circuit (A matrix display with N rows and M columns needs (N+M) drivers). It is preferable to reduce the number of intervals in a cycle to reduce the error due to distortion in the addressing waveforms so that the select time will increase (for a given refresh rate) and therefore RC time constant will be small as compared to the duration of the select time and thereby reduce the error in the RMS voltage. Amplitude modulation [3] and pulse height modulation [4] can display a large number of gray shades with a minimum number of time intervals. However, the number of voltages in the data waveforms is large. For example, the amplitude modulation that is based on line-by-line addressing has the least number of voltages in the addressing waveforms (i.e.2(G−1)to display G gray shades) among these techniques. It is much higher for the pulse height modulation that is based on multi-line addressing. Either the hardware complexity of the drivers is high as in case of digital type drivers with analog multiplexers and digital to analog converters or the power consumption is high as in case of analog type data drivers when amplitude modulation and pulse height modulation are used for displaying gray shades. Successive approximation [5]-[6] technique can be used to display a large number of gray shades with simple drivers. The number of time intervals is equal to the smallest integer value that is equal to or greater than logarithm of the number of gray shades i.e. log2 G. Similarly wavelet based addressing techniques can display large number of gray shades. Number of time intervals necessary is about the same order for the wavelets based techniques for displaying gray shades [7]-[12]. Both the techniques have less number of voltages in the addressing waveforms as compared to amplitude and pulse height modulation techniques and therefore the hardware complexity of the drivers is also less as compared to amplitude and pulse height modulation. It is preferable to meet the following conditions when gray shades are displayed in passive matrix liquid crystal displays:                a. Number of time intervals in a cycle is small so that a large number of gray shades can be displayed without flicker and achieve good brightness uniformity among pixels that are driven to the same gray shade.        b. As few voltages as possible in the addressing waveforms so that the hardware complexity and the cost of driver circuit will be low.        
The successive approximation technique and the wavelets based addressing techniques meet this criterion to some extent. FIG. 1 shows the typical waveforms of successive approximation technique and FIG. 2 shows the typical waveform of wavelets based technique for displaying gray shades in liquid crystal display. The number of voltages in the scanning and data waveforms is also less for these techniques and therefore the hardware complexity of the drivers is also less as compared to that of amplitude modulation and pulse height modulation techniques. The main objective of this invention is to reduce the number of time intervals to complete a cycle and achieve more number of gray shades with simple waveforms having less number of voltages as compared to that of sussessive approximation and wavelets based techniques.